The invention relates generally to computing energy transfer from particles to a surface, thereby causing ablation. In particular, numerical methods for augment heat transfer from flow-fields to wall surfaces by accounting for particle collision kinetic and thermal effects against the surface.
The United States Navy employs ablative materials missile launching systems to protect the surfaces of the launcher structure, with the Mk 41 Vertical Launching System (VLS) representing one such example contained aboard a combat vessel as its platform. Several missiles are contained within the VLS for selective launching, each by its rocket motor booster. Upon igniting a rocket motor within a VLS canister, high-temperature exhaust, often containing aluminum oxide (Al2O3) particles, flows through the gas management system and over ablative materials that cover protected surfaces. The ablative material chars and/or erodes as the launcher surfaces absorb energy from the exhaust gas and particles. The erosion protects the launcher structure by decreasing the amount of heat transferred through the ablative to the underlying structures.
The energy imparted to the ablative wall may come from convection from the gas or from particle effects. Particles may impart energy to the walls from conduction and solidification during impacts and from abrasion due to repeated particle impacts. The extent of the ablative erosion depends on the type of rocket launched and the duration of time the missile remains within the canister. The most significant erosion occurs during a restrained firing, when the rocket motor is ignited but the missile cannot exit the canister.
Analytical, experimental, and computational methods have been used to predict the amount of erosion that occur during a rocket launch or restrained firing, and these prediction methods have provided valuable information regarding ablation erosion for launcher designs. However, large errors can result from comparisons between predictions and measured erosion data. There have also been a few occurrences of the rocket exhaust eroding through all the ablative material and burning through the launcher structure. Improved computational methods to predict the extent of ablative erosion would allow for improved safety and reliability of U.S. Navy missile launching systems. The code described in this report is an attempt to improve prediction capabilities.
Naval Surface Warfare Center, Dahlgren Division (NSWCDD) has been involved in predicting VLS ablation for many years. See C. T. Boyer, J. W. Powers, T. R. Burgess, J. R. Bowen and K. R. Stull, “High-Strength Quartz Reinforcement for Mk 41 Vertical Launching System Ablators”, NSWCDD/TR-95/224, Naval Surface Warfare Center, Dahlgren Division, 1996. The conventional method for predicting erosion requires both experimental and computational results. Conventional techniques provide a computational fluid dynamics (CFD) analysis of the gas dynamics within the VLS plenum and uptake.
Although the rocket exhaust may have Al2O3 particles, the CFD analysis does not include the particle motion within the gas flow. Computational power has not been sufficient to produce a coupled particle-gas CFD solution in a reasonable amount of time. To account for the added mass of the particles within the flow, the exhaust gas is modeled as a “heavy” gas. The heavy gas is a mixture of the gaseous exhaust products and Al2O3 with the proportions set to provide the correct total exhaust mass flow rate. This heavy gas is conventionally used to provide a simulation flow field within the launcher.
Using the conventional CFD results, a computational heat flux from the hot gas to the launcher walls is estimated. In order to accurately compute a heat flux using CFD, the boundary layer must be fully resolved. For geometries of the scale and complexity of the VLS, using a grid this fine typically requires prohibitively long run times for the CFD solution. Therefore, the heat flux is computed from gas properties taken at a “standoff” distance from the wall.
Next, an empirical relation is used to scale the computational heat flux. The empirical relation was derived from erosion measurements obtained from a set of experiments designed to investigate the performance of different ablative materials. The scaled heat flux is then used in a one-dimensional heat conduction code to compute the steady-state wall ablation rate. The total wall ablation is applied as the steady-state ablation rate multiplied by the total burn time of the rocket motor. Errors in this conventional predicted ablation may be on the order of several hundred percent.